The VMLMB algorithm for large scale optimization with bound constraints

This repository provides implementations of the VMLMB algorithm and preconditioned linear conjugate gradient method in various high-level programming languages.

VMLMB (for Variable Metric Limited Memory with Bounds) is a quasi-Newton optimization method with small memory requirements and which may take into account separable bound constraints. This algorithm is of particular interest for minimizing a smooth cost function of a potentially very large number of variables (millions or billions) possibly under bound constraints. VMLMB has been successfully used to solve many different kinds of problems notably image restoration in inverse problems framework.

The objective of this repository is to provide algorithms that:

• run out of the box (no additional libraries needed);
• are efficient (although maybe not as fast as if implemented in a low level compiled language) and usable for serious applications;
• are well documented;
• have readable code;
• can be easily modified.

Contents

The repository is organized as follows:

• Directory matlab contains a pure Matlab/GNU Octave version of VMLMB and of a preconditioned linear conjugate gradient method. See file matlab/README.md for installation and usage instructions.

• Directory python contains a pure NumPy version of VMLMB and of a preconditioned linear conjugate gradient method. See file python/README.md for installation and usage instructions.

• Directory yorick contains a pure Yorick version of VMLMB and of a preconditioned linear conjugate gradient method. See file yorick/README.md for installation and usage instructions.

References

• Hestenes, M. R. & Stiefel, E. "Methods of Conjugate Gradients for Solving Linear Systems," in Journal of Research of the National Bureau of Standards, 49, pp. 409-436 (1952).

• É. Thiébaut, "Optimization issues in blind deconvolution algorithms," in Astronomical Data Analysis II, SPIE Proc. 4847, 174-183 (2002).